ZBrush has this feature by default; as you sculpt, whatever point you last touched becomes the orbit pivot for the camera.
It’s very useful when the bit you’re sculpting is far from the object pivot and you’re zoomed in, otherwise you’re constantly rotating and panning, rotating and panning etc to keep the bit you’re sculpting in view.
I thought this might be an option in the general settings or camera settings, but I tried a few things, nothing seemed to work. I hope I’m wrong!
Have you tried to touch the object shortly, and rotate the camera after? It does exactly what you are requesting imho.
Under the gear icon, you can find “show small dot” option. Wether it is ticked or not, this is the camera pivot and you change it by tapping somewhere on the object.